-calculus, a model
of uniformly
concurrent computation. It integrates eager and lazy functional
computation and describes the intended complexity behavior
in both cases.
,
if result, termination and complexity are independent from
the computation order. We establish theses properties for the
-calculus by proving its
uniform confluence.
-calculus extends to models
of concurrent
computation providing for consumable resources and indeterminism.
Such are the -calculus, a
foundation of concurrent
computation with constraints, and the -calculus, a
successor of CCS based on channel communication.
-calculus is a relational
calculus with procedural
abstraction and application. It provides for communication
over logic variables and for suspension on their instantiation.
Both mechanisms come naturally with parallel composition
and declaration.
We embed the eager and the lazy -calculus
into the -calculus. Using
explicit references
we guarantee that functional arguments are evaluated
at most once. Explicit references are a special form
of logic variables. These are needed too for
representing lazy functional control.
We prove the adequacy of the embedding of the eager
-calculus with respect to termination and
complexity. We conjecture that the embedding of
the lazy -calculus preserves termination
and improves complexity.